H. F. Chau

Is Quantum Bit Commitment Really Possible

Work on quantum cryptography was started by S. J. Wiesner in a paper written in about 1970, but remained unpublished until 1983 [1]. Recently, there have been lots of renewed activities in the subject. The most wellknown application of quantum cryptography is the socalled quantum key distribution (QKD) [2–4], which is useful for making communications between two users totally unintelligible to an eavesdropper. QKD takes advantage of the uncertainty principle of quantum mechanics: Measuring a quantum system in general disturbs it. Therefore, eavesdropping on a quantum communication channel will generally leave unavoidable disturbance in the transmitted signal which can be detected by the legitimate users. Besides QKD, other quantum cryptographic protocols [5] have also been proposed. In particular, it is generally believed [4] that quantum mechanics can protect private information while it is being used for public decision. Suppose Alice has a secret x and Bob a secret y. In a “two-party secure computation” (TPSC), Alice and Bob compute a prescribed function f(x,y) in such a way that nothing about each party’s input is disclosed to the other, except for what follows logically from one’s private input and the function’s output. An example of the TPSC is the millionaires’ problem: Two persons would like to know who is richer, but neither wishes the other to know the exact amount of money he/she has. In classical cryptography, TPSC can be achieved either through trusted intermediaries or by invoking some unproven computational assumptions such as the hardness of factoring large integers. The great expectation is that quantum cryptography can get rid of those requirements and achieve the same goal using the laws of physics alone. At the heart of such optimism has been the widespread belief that unconditionally secure quantum bit commitment (QBC) schemes exist [6]. Here we put such optimism into very serious doubt by showing

Efficient Quantum Key Distribution Scheme and a Proof of Its Unconditional Security

AbstractWe devise a simple modification that essentially doubles the efficiency of the BB84 quantum key distribution scheme proposed by Bennett and Brassard.We also prove the security of our modified scheme against the most general eavesdropping attack that is allowed by the laws of physics. The first major ingredient of our scheme is the assignment of significantly different probabilities to the different polarization bases during both transmission and reception, thus reducing the fraction of discarded data. A second major ingredient of our scheme is a refined analysis of accepted data: We divide the accepted data into various subsets according to the basis employed and estimate an error rate for each subset separately. We then show that such a refined data analysis guarantees the security of our scheme against the most general eavesdropping strategy, thus generalizing Shor and Preskill’s proof of security of BB84 to our new scheme. Until now, most proposed proofs of security of single-particle type quantum key distribution schemes have relied heavily upon the fact that the bases are chosen uniformly, randomly, and independently. Our proof removes this symmetry requirement.

Weighted assortative and disassortative networks model

Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by topological growth as well as by weight change. In addition, we introduce the weighted assortativity coefficient, which generalizes the assortativity coefficient of a topological network, to measure the tendency of having a high-weighted link between two vertices of similar degrees. Network generated by our model exhibits scale-free behavior with a tunable exponent. Besides, a few non-trivial features found in real-world networks are reproduced by varying the parameter ruling the speed of weight evolution. Most importantly, by studying the weighted assortativity coefficient, we found that both topologically assortative and disassortative networks generated by our model are in fact weighted assortative.

Practical issues in quantum-key-distribution postprocessing

Quantum key distribution (QKD) is a secure key generation method between two distant parties by wisely exploiting properties of quantum mechanics. In QKD, experimental measurement outcomes on quantum states are transformed by the two parties to a secret key. This transformation is composed of many logical steps (as guided by security proofs), which together will ultimately determine the length of the final secret key and its security. We detail the procedure for performing such classical postprocessing taking into account practical concerns (including the finite-size effect and authentication and encryption for classical communications). This procedure is directly applicable to realistic QKD experiments and thus serves as a recipe that specifies what postprocessing operations are needed and what the security level is for certain lengths of the keys. Our result is applicable to the BB84 protocol with a single or entangled photon source.

Making an empty promise with a quantum computer

Alice has made a decision in her mind. While she does not want to reveal it to Bob at this moment, she would like to convince Bob that she is committed to this particular decision and that she cannot change it at a later time. Is there a way for Alice to get Bobs trust? Until recently, researchers had believed that the above task can be performed with the help of quantum mechanics. And the security of the quantum scheme lies on the uncertainty principle. Nevertheless, such optimism was recently shattered by Mayers and by us, who found that Alice can always change her mind if she has a quantum computer. Here, we survey this dramatic development and its implications on the security of other quantum cryptographic schemes. PACS numbers: 03.65.Bz, 89.70.+c, 89.80.+h

Universal squash model for optical communications using linear optics and threshold detectors

Transmission of photons through open-air or optical fibers is an important primitive in quantum-information processing. Theoretical descriptions of this process often consider single photons as information carriers and thus fail to accurately describe experimental implementations where any number of photons may enter a detector. It has been a great challenge to bridge this big gap between theory and experiments. One powerful method for achieving this goal is by conceptually squashing the received multiphoton states to single-photon states. However, until now, only a few protocols admit a squash model; furthermore, a recently proven no-go theorem appears to rule out the existence of a universal squash model. Here we show that a necessary condition presumed by all existing squash models is in fact too stringent. By relaxing this condition, we find that, rather surprisingly, a universal squash model actually exists for many protocols, including quantum key distribution, quantum state tomography, Bells inequality testing, and entanglement verification.

Practical entanglement distillation scheme using recurrence method and quantum low density parity check codes

Many entanglement distillation schemes use either universal random hashing or breeding as their final step to obtain almost perfect shared EPR pairs. In spite of a high yield, the hardness of decoding a random linear code makes the use of random hashing and breeding infeasible in practice. In this pilot study, we analyze the performance of the recurrence method, a well-known entanglement distillation scheme, with its final random hashing or breeding procedure being replaced by various efficiently decodable quantum codes. Among all the replacements investigated, the one using a certain adaptive quantum low density parity check (QLDPC) code is found to give the highest yield for Werner states over a wide range of noise level—the yield for using this QLDPC code is higher than the first runner up by more than 25% over a wide parameter range. In this respect, the effectiveness of using QLDPC codes in practical entanglement distillation is illustrated.

ONE-WAY FUNCTIONS IN REVERSIBLE COMPUTATIONS

One-way functions are used in modern crypto-systems as doortraps because their inverse functions are supposed to be difficult to compute. Nonetheless with the discovery of reversible computation, it seems that one may break a one-way function by running a reversible computer backward. Here, we argue that reversible computation alone poses no threat to the existence of one-way functions because of the generation of “garbage bits” during computations. Consequently, we prove a necessary and sufficient condition for a one-to-one function to be one-way in terms of the growth rate of the total number of possible garbage bit configurations with the input size.

Reply to "comment on 'quantum string seal is insecure'"

In Phys. Rev. A 76, 056301 (2007), He claimed that the proof in my earlier paper [Phys. Rev. A 75, 012327 (2007)] is insufficient to conclude the insecurity of all quantum string seals because my measurement strategy cannot obtain nontrivial information on the sealed string and escape detection at the same time. Here, I clarify that our disagreement comes from our adoption of two different criteria on the minimum amount of information a quantum string seal can reveal to members of the public. I also point out that He did not follow my measurement strategy correctly.

MINORITY GAME WITH INERTIAL AGENTS

Many agents in the real world are reluctant to change their mind. Such an “inertial” behavior may affect the dynamics and cooperation of agents. Here we study the effect of “inertia” in the framework of Minority Game by requiring agents to choose their strategies via hypothesis testing. We find both numerically and semi-analytically that the presence of “inertial” agents greatly improves global cooperation of the system.